The cavity inside a neutral conducting spherical shell of inner radius a and outer radius b is f illed with an insulating material that has uniform charge density ρ > 0. (a) Find the electric potential as a function of r in every region of space taking V(r → ∞) = 0. Hint:Find the electric field first using Gauss' Law and start finding the potential in the region r > b towork your way inwards.(b) Test your results from (a) by finding the known electric field usingE = -ᎥᏙƏr-f.(c) A point charge q> 0 with mass m is moving towards the center of the sphere. What is the speedof this point charge at r = 2b if it were to barely touch the outer surface of the shell before turningback?

Given:Charge density,ρr = ρ for r<a0 for r≥ar<a is an insilatorspherical shell from r≥a to…

Answered: The cavity inside a neutral conducting…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter5: Gravitation

Section: Chapter Questions

Problem 5.10P

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Question

The cavity inside a neutral conducting spherical shell of inner radius a and outer radius b is f illed with an insulating material that has uniform charge density ρ > 0.

(a) Find the electric potential as a function of r in every region of space taking V(r → ∞) = 0. Hint:
Find the electric field first using Gauss' Law and start finding the potential in the region r > b to
work your way inwards.
(b) Test your results from (a) by finding the known electric field using
E = -
ᎥᏙ
Ər
-f.
(c) A point charge q> 0 with mass m is moving towards the center of the sphere. What is the speed
of this point charge at r = 2b if it were to barely touch the outer surface of the shell before turning
back?

Expert Solution

Step 1

$\begin{array}{l} G i v e n : \\ C h a r g e d e n s i t y, \\ ρ (r) = \{\begin{matrix} ρ f o r r < a \\ 0 f o r r \geq a \end{matrix} \\ r < a i s a n i n s i l a t o r \\ s p h e r i c a l s h e l l f r o m r \geq a t o r \leq b i s c o n d u c t o r \end{array}$

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